Time-Varying Delayed <i>H</i>_∞ Control Problem for Nonlinear Systems: A Finite Time Study Using Quadratic Convex Approach

Abstract

In this manuscript, we consider the finite-time H ∞ control for nonlinear systems with time-varying delay. With the assistance of a novel Lyapunov-Krasovskii functional which includes some integral terms, a matrix-based on quadratic convex approach, combined with Wirtinger inequalities and some useful integral inequalities, a sufficient condition of finite-time boundedness is established. A novel feature presents in this paper is that the restriction which is necessary for the upper bound derivative is not restricted to less than 1. Further a H ∞ controller is designed via memoryless state feedback control and a new sufficient conditions for the existence of finite-time H ∞ state feedback for the system are given in terms of linear matrix inequalities (LMIs). At the end, some numerical examples with simulations are given to illustrate the effectiveness of the obtained result.

Keywords

• finite-time <i>H</i>_∞ control
• nonlinear system
• time-varying delay
• linear matrix inequalities (LMIs)
• Lyapunov-Krasovskii functional (LKF)